An unknotting result for complete minimal surfaces in \(\mathbb{R}^ 3\)
type: Item
instance of: scholarly article
title: An unknotting result for complete minimal surfaces in \(\mathbb{R}^ 3\)
zbMATH Open document ID: 0773.53003
DOI: 10.1007/BF01232017
published in: Inventiones Mathematicae
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/144011
review text: The main theorem describes the closed connected complementary components of a complete properly embedded minimal surface in 3-space. They are either metrically \(\mathbb{R}^ 2\times[0,h]\) or, up to diffeomorphism, made from an at most countable collection of specified building blocks with a proper collection of handles attached. The proof uses the plane theorem of do Carmo, Peng and Fischer-Colbrie/Schoen and topological methods developed by Meeks, Yau and others.
reviewed by: Dirk Ferus
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 126370
zbMATH Keywords: plane theorem
zbMATH Keywords: stability
zbMATH Keywords: handlebody
author: Michael Freedman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 126370